Thread: orbit

Suppose and have the same pattern. Prove that .

Now an orbit of and element in is all the "possible stuff" that a permutation can map to. So does imply that they are in the same orbit?

Originally Posted by Sampras

Suppose and have the same pattern. Prove that .

Now an orbit of and element in is all the "possible stuff" that a permutation can map to. So does imply that they are in the same orbit?

I'm sorry. Maybe some other member will swoop in and help you. But if not, I just have two questions. What does 'pattern' mean in this context? and what is represent. Also, what is ? Just some group under consideration? If so, then does not mean that or vice versa (which is really the same thing).

Originally Posted by Sampras

Suppose and have the same pattern. Prove that .

Now an orbit of and element in is all the "possible stuff" that a permutation can map to. So does imply that they are in the same orbit?

If you don't properly define your "stuff" people won't properly understand it: what are f,g? What is a "pattern" for them? What is W(f)? What is X?
What action of what group (presumably ) on what set are we talkin about here?

Tonio